1 The author is with the State Key
Laboratory of Networking and Switching Technology, Beijing University of Posts and
Telecommunications, Beijing
100876, P.R.
China.
whj409@163.com2 The author is with the State Key
Laboratory of Networking and Switching Technology, Beijing University of Posts and
Telecommunications, 100876
Beijing, P.R.
China 3 The author is with School of Science,
Beijing University of Posts and Telecommunications, 100876
Beijing, P.R.
China

Received:
3
July
2012
Accepted:
26
September
2013

Abstract

The Legendre symbol has been used to construct sequences with ideal cross-correlation,
but it was never used in the arithmetic cross-correlation. In this paper, a new class of
generalized Legendre sequences are described and analyzed with respect to their period,
distributional, arithmetic cross-correlation and distinctness properties. This analysis
gives a new approach to study the connection between the Legendre symbol
and the arithmetic cross-correlation. In the end of this paper, possible application of
these sequences with optimal arithmetic cross-correlation is indicated.

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